In this paper, a single parameter family of hybrid ellipsoid-dumbbell models is proposed for the hydrodynamic behavior of a polymer molecule in dilute solutions. The model allows for rotation and partial deforming of molecule, but not for bending. The periodic fluctuations and shear thinning have been obtained by numerically integrating the equations of motion over a wide range of the dimensionless parameter, a ratio of polymer-spring and solvent-viscosity forces. The results show that the rotation frequency decreases with the increasing shear rate because of the deformation effect, which increase the stability of flow. The effects of polymer additives on flow viscosity and its application are also discussed. These results will be significant for drag reduction mechanism.